Angle-Preserving Quadrilateral Mesh Parameterization.

Abstract

In response to their growing use in the real world, this article presents two algorithms for direct parameterization of quadrilateral meshes. The proposed algorithms are angle-preserving mappings, with one mapping a topological disk surface onto a Euclidean plane and one mapping a topological sphere surface onto a unit sphere. Specifically, for topological disk surfaces, the authors devise a discrete conformal energy function to flatten the quadrilateral meshes with a length-preserving boundary condition. For topological sphere surfaces, a derived Tuette energy function is applied to the initialization of parameterization for a mesh, and then the final spherical parametrization result is obtained by minimizing a devised harmonic energy function. Experimental results demonstrate the efficiency of the proposed methods.